Regional geomagnetic field modelling method based on a two-stage adaptive weight physics-informed neural network

Accurate and rapid prediction of structural responses to seismic loading is critical for ensuring structural safety. Recently, there has been active research focusing on the application of deep learning techniques, including Physics-Informed Neural Networks (PINNs) and Long Short-Term Memory (LSTM) networks, to predict the dynamic behavior of structures. While these methods have shown promise, each comes with distinct limitations. PINNs offer physical consistency but struggle with capturing long-term temporal dependencies in nonlinear systems, while LSTMs excel in learning sequential data but lack physical interpretability. To address these complementary limitations, this study proposes a hybrid LSTM-PINN model, combining the temporal learning ability of LSTMs with the physics-based constraints of PINNs. This hybrid approach allows the model to capture both nonlinear, time-dependent behaviors and maintain physical consistency. The proposed model is evaluated on both single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF) structural systems subjected to the El-Centro ground motion. For validation, the 1940 El-Centro NS earthquake record was used, and the ground acceleration data were normalized and discretized for numerical simulation. The proposed LSTM-PINN is trained under the same conditions as the conventional PINN models (e.g., same optimizer, learning rate, and loss structure), but with fewer training epochs, to evaluate learning efficiency. Prediction accuracy is quantitatively assessed using mean error and mean squared error (MSE) for displacement, velocity, and acceleration, and results are compared with PINN-only models (PINN-1, PINN-2). The results show that LSTM-PINN consistently achieves the most stable and precise predictions across the entire time domain. Notably, it outperforms the baseline PINNs even with fewer training epochs. Specifically, it achieved up to 50% lower MSE with only 10,000 epochs, compared to the PINN's 50,000 epochs, demonstrating improved generalization through temporal sequence learning. This study empirically validates the potential of physics-guided time-series AI models for dynamic structural response prediction. The proposed approach is expected to contribute to future applications such as real-time response estimation, structural health monitoring, and seismic performance evaluation.

The geometric bone model of patients is an important basis for individualized biomechanical modeling and analysis, formulation of surgical planning, design of surgical guide plate, and customization of artificial joint. In this study, a rapid three-dimensional (3D) reconstruction method based on statistical shape model was proposed for femur. Combined with the patient plain X-ray film data, rapid 3D modeling of individualized patient femur geometry was realized. The average error of 3D reconstruction was 1.597-1.842 mm, and the root mean square error was 1.453-2.341 mm. The average errors of femoral head diameter, cervical shaft angle, offset distance and anteversion angle of the reconstructed model were 0.597 mm, 1.163°, 1.389 mm and 1.354°, respectively. Compared with traditional modeling methods, the new method could achieve rapid 3D reconstruction of femur more accurately in a shorter time. This paper provides a new technology for rapid 3D modeling of bone geometry, which is helpful to promote rapid biomechanical analysis for patients, and provides a new idea for the selection of orthopedic implants and the rapid research and development of customized implants.

Self-adaptive loss balanced Physics-informed neural networks

Accurate forecasting of the lifetime and degradation mechanisms of lithium-ion batteries is crucial for their optimization, management, and safety while preventing latent failures. However, the typical state estimations are challenging due to complex and dynamic cell parameters and wide variations in usage conditions. Physics-based models need a tradeoff between accuracy and complexity due to vast parameter requirements, while machine-learning models require large training datasets and may fail when generalized to unseen scenarios. To address this issue, this paper aims to integrate the physics-based battery model and the machine learning model to leverage their respective strengths. This is achieved by applying the deep learning framework called physics-informed neural networks (PINN) to electrochemical battery modeling. The state of charge and state of health of lithium-ion cells are predicted by integrating the partial differential equation of Fick’s law of diffusion from a single particle model into the neural network training process. The results indicate that PINN can estimate the state of charge with a root mean square error in the range of 0.014% to 0.2%, while the state of health has a range of 1.1% to 2.3%, even with limited training data. Compared to conventional approaches, PINN is less complex while still incorporating the laws of physics into the training process, resulting in adequate predictions, even for unseen situations.

Volume-resolving imaging techniques are rapidly advancing progress in experimental fluid mechanics. However, reconstructing the full and structured Eulerian velocity and pressure fields from under-resolved and noisy particle tracks obtained experimentally remains a significant challenge. We {adopt and characterize} a method based on Physics-Informed Neural Networks (PINNs). In this approach, the network is regularized by the Navier-Stokes equations to interpolate the velocity data and simultaneously determine the pressure field. We compare this approach to the state-of-the-art Constrained Cost Minimization method. Using data from direct numerical simulations and various types of synthetically generated particle tracks, we show that PINNs are able to accurately reconstruct both velocity and pressure even in regions with low particle density and small accelerations. We analyze both the root mean square error of the reconstructions as well their energy spectra. PINNs are also robust against increasing the distance between particles and the noise in the measurements, when studied under synthetic and experimental conditions. Both the synthetic and experimental datasets used correspond to moderate Reynolds number flows. Three-dimensional three-component (3D-3C) particle imaging velocimetry can be set up even with a single camera when volumetric color-coded illumination is applied to the measurement space. The idea itself was very old as reported a lot in early PIV conferences in 1990s. However, most of PIV developers abandoned to make it feasible in those days due to various limitations struggled for quantitative color extraction required to capture the displacement of color-dependent particle coordinates. Our team spent a long time to overcome such problems to date and reached a certain level of feasibility gradually approaching to tomographic PIV. Our efforts to improve the measurement performance are i) algorithm for easy color calibration, ii) multi-cycle color illumination, iii) intentional particle defocusing, iv) animated color coding, and v) introduction of artificial neural network. In the seminar, I will explain these techniques and their applications including delta-wing wakes, boundary layer on rough surfaces, flows behind wind turbine, wall-impinging vortex rings, and thermal turbulence.

The RELAP5 code, designed to predict the behavior of reactor systems during accident conditions, is used widespread over the world. This work aims to show and describe the RELAP-MV graphical software developed using computer language (XML) and Visualized Modularization software technology to recognized best estimated transient simulation program of Light water reactor, in combination with new options for improved modeling methods, advanced programming, computational simulation techniques and integrated graphics displays. RELAP5 code is complex and inconvenient for utilizing method of data cards and close logic relationship of data in input file. The main purpose of developing RELAP5-MV is to simplify progress and increase simulation efficiency. Traditional modeling method and modular modeling method are supported with RELAP5-MV to achieve aims of device and system simulation. For traditional modeling method, all kinds of components are developed such as single volume, single junction, pipe, branch, time dependent volume, etc. For modular modeling method, the module library is established in the software. The library packages include the main system equipments of primary and secondary loops such as reactor core, U tube steam generator, once through steam generator, pump, pressurizer, steam turbine, condenser, heat exchanger, deaerator, etc. in a pressurized water reactor, which can be analyzed and modeled in details. From the library the capabilities are easy to select icons interface from the library packages. The analysis results show that the software can effectively simulate nuclear power system by RELAP5. Plot and data binding function is supported for post-processing of calculation result. Personal computer interface of RELAP5-MV makes it more convenient, fast and visualized in simulation system establishing process. Performance Relap5 related analysis activities, such as creating and modifying input file, viewing component division figures and generating output files can be realized by RELAP5-MV. The interactive simulation interface feature allows the users to simulate specific reactor transients and accidents — such as LOCA, LOFA, scram, etc. Accuracy and reliability of RELAP5-MV have already been confirmed by simulating main coolant system of Pressurize Water Reactor (PWR) and modeling efficiency increases significantly by using RELAP5-MV. Visualization modeling, analysis and computational simulation for thermal hydraulic analysis of nuclear reactor can not only lower the RELAP5 threshold but also improve the efficiency of nuclear science research greatly, and also promoting the development of related research in RELAP5 safety analysis. RELAP5-MV can give an approach to build, verify and assess simulation design of reactor power system.

Physics-informed neural networks (PINNs) solve partial differential equations (PDEs) by embedding physical conditions as soft penalties into the loss function. However, the coexistence of multiple loss components often leads to gradient conflicts, degrading convergence and solution accuracy. To address this issue, we propose a dynamic domain–gradient loss reweighting PINN (DDR-PINN). The proposed method introduces a dual-residual reweighting mechanism based on gradient variations, where adaptive weights are derived from the L2 norm of the dot product between loss gradients and residuals. These weights are further normalized through a nonlinear hyperbolic tangent transformation, enabling dynamic and balanced reweighting of interior, initial, and boundary domain losses throughout training. Extensive numerical experiments on PDEs with both Dirichlet and Neumann boundary conditions demonstrate that the DDR-PINN consistently outperforms the standard PINN, APINN, and VI-PINN with the fewest trainable parameters.

Designing a fusion power plant is a complex task, given the intricate nature of its components and the extensive range of design parameters involved. Simulation plays a crucial role in predicting the performance of fusion reactor components through the life cycle, with the coupling of neutronics with thermal analysis being vital for the design and optimization of various systems such as the blanket module and the vacuum vessel wall. Given the extensive design space for these parts and the diverse requirements of fusion components, there is a pressing need for rapid and precise prediction of specific physics fields to check whether the design satisfies the engineering requirements. This paper introduces physics-informed neural networks as surrogate models to resolve the temperature field of the vacuum vessel wall due to neutronics heating. This research demonstrates the capability of physics-informed neural networks for the rapid prediction of physical fields whilst maintaining good accuracy, with a L2 relative error of 0.0093. The output of this research could be used as a template for further developments in surrogate model based simulation-driven engineering in the fusion industry. • The paper describes the use of two physics-informed neural networks to estimate vacuum vessel wall temperature due to neutronics heating. • The work demonstrates that physics-informed neural networks can be used where heating is non-uniform and has high gradients. • The predictions made by the physics-informed neural networks compare well with results obtained using the finite element method.

The classical step-by-step integration method is commonly used for solving structural dynamic responses, but its performance is highly sensitive to the choice of time step. A large time step can significantly reduce accuracy and stability, while a very small time step greatly diminishes computational efficiency. Data-driven modeling and analysis methods are particularly favored for their potential to replace traditional structural analysis methods. However, traditional data-driven machine learning approaches require substantial amounts of training data to predict structural dynamic responses. Moreover, these methods often function as black boxes, lacking physical interpretability, and acquiring the necessary data can be challenging in practice. To address these limitations, this paper employs a physics-informed neural network (PINN) method for structural dynamic response analysis. The PINN approach incorporates the governing equations of structural dynamics into the neural network’s loss function as physical constraints, endowing the model with physical interpretability. The feasibility and effectiveness of this method are demonstrated through case studies on structural dynamic responses under different excitation scenarios. Numerical results show that the PINN method can accurately analyze structural dynamic responses without relying on system response data, a key advantage over traditional data-driven models. Moreover, unlike the classical step-by-step integration method, the PINN approach operates as a spatial domain optimization process and is independent of time step. Given the critical role of hyperparameters in the performance of the PINN model, this paper systematically investigates the influence of various hyperparameter settings on accuracy and efficiency, uncovering patterns of their impact on structural response analysis. Replication code for this paper will be available on GitHub:https://github.com/duke-iem/AIStructDynSolve.

There are many methods in building local geomagnetic field, such as polynomial method, interpolation method, Spherical Cap Harmonic Analysis and Rectangular Harmonic Analysis. Curve Surface Spine Function and Multi-surface Function are two interpolation methods. The model based on interpolation passes each node compared with fitting method. It can be proved that the interpolation method can get more accurate result compared with polynomial fitting method in building the local marine geomagnetic field model. The issue which should be researched in multi-surface function are quality control of geomagnetic data, kernel function choice, choice of the smoothing factor, model node selecting and zoning modeling method. The quality control of geomagnetic data is very important in building local marine geomagnetic field, here we introduce a kind of trend-surface methods for the quality control. The method establishes a function relative to location and uses 2sigma/3sigma principle to remove the gross error of geomagnetic data. It is proved to be very efficient in the filtering. The kernel function normally used are hyperboloid function and inverted hyperboloid function. Which one adopted in building the model needs to be verified in actual application. By experiment, we found that the accuracy of the model is higher using hyperboloid function than using inverted hyperboloid function. Smoothing factor is another important parameters in building local geomagnetic field model. Smoothing factor can improve the curvature of the model surface. Optimum smoothing factor is also required to be verified and determined in actual applications. We can find that the model's accuracy improving with the smoothing factor change from 0 to 100. We can also find there is an inflexion in the change of model accuracy. The hyperboloid function model's accuracy changes little with smoothness factor, but for the inverted hyperboloid function, corresponding model accuracy is very sensitive to smoothness factor. The model's accuracy is improved with the increase of node number. But the computational complexity will be increased with the node number increasing, and at the same time will lead to the unstable solution in building geomagnetic field model. Thus the node number should be appropriate in building the model. Generally, we only need small number of geomagnetic data in building the local geomagnetic field model with uniform change. However, a large number of geomagnetic data is required when geomagnetic change is more complicated. Character node is very important in building precise local geomagnetic field model. Character node represents its' surrounding geomagnetic field change. By experiment, we found that the accuracy of model constructed with selected the character node was better than that built with random geomagnetic data, especially in which geomagnetic field changes sharply. Zoning modeling method can avoid the problem, which too large nodes number lead to computational complexity in large area. The model's accuracy can be improved distinctly if we use enough and high-quality geomagnetic data. Because the model surface passes each node in building the model using Multi-surface Function, thus it can guarantee the smoothness and continuity in the common area of two adjoin modeling zones. Geomagnetic data of a marine area with 11-kilometer length and 1-kilometer width is used for the study of building local marine geomagnetic field model. In the study, we adopt above research methods and achieve the model accuracy with 8.09 nT of root mean square (RMS) in whole area. We also implement a zoning modeling experiment. In the experiment, we divide the whole area into 5 subsections, build models in these subsections, and achieve the model's accuracy with 5.29 nT in the whole area. Comparing above statistic parameters, we can find that the zoning modeling method is a kind of ideal methods in building high-accuracy local marine geomagnetic field model.

Establishing a mathematical model of a Francis turbine is the foundation for the simulation of hydropower station operation and is of great significance for the analysis of the hydropower station’s transient process. Currently, in engineering practice, the model is often established based on the comprehensive characteristic curves of the Francis turbine provided by the manufacturer, using the external characteristic method. Traditional modeling methods mostly adopt manual reading of points or the use of dedicated numerical software for curve tracing to discretely sample the comprehensive characteristic curves of the turbine. This method is labor-intensive, inefficient, and relies on manual experience, with a small sample size, which, to some extent, affects the accuracy and reliability of the numerical processing results and cannot meet the needs of transient process simulation analysis. To address these shortcomings, this paper proposes a refined modeling method based on image numerical processing and an RBF neural network. Taking the HLA685 Francis turbine as an example, the method first uses image processing to achieve large-scale automated discrete sampling of the turbine’s high-efficiency zone characteristic data, then reasonably extends the small-opening and low-speed regions, and finally uses the RBF neural network method for interpolation and extrapolation to obtain the full characteristic data. This method can effectively improve the efficiency and accuracy of comprehensive characteristic modeling of the turbine and has good reference significance for the comprehensive characteristic modeling of blade-type machinery.

To accurately reflect the switching characteristics of GaN High Electron Mobility Transistor (GaN HEMT), this article proposes a fast and accurate Spice circuit simulation model of GaN HEMT. The model mainly imports the saturation current modulation factor $\theta_{(V g s)}$) and focuses on the modeling accuracy of the nonlinear capacitance $C_{\text{g}\text{d}}$, which would affect the switching process. In addition, to address the present problems of relying on commercial fitting software with high copyright fees for parameter extraction and extracting model parameters very intricately by traditional modeling methods, a combined optimization method is proposed to extract the model parameters for modeling. The combined algorithm is based on the Genetic algorithm of global optimization and the Levenberg-Marquardt algorithm of the local optimum and it has the advantages of the global optimal solution and fast convergence. The proposed modeling method is verified to be fast and accurate by building a Double-Pulse Test experimental platform and comparing the simulated and experimental waveforms of the dynamic and static characteristics of GaN HEMT.

Ground reaction force (GRF) estimation during gait is essential for analyzing human locomotion. Though several conventional machine learning models have been proposed for GRF estimation, their dependence on data often limits generalizability and prediction accuracy. To address these limitations, the present study explores the feasibility of Physics-Informed Neural Networks (PINNs) for GRF estimation. The developed PINN model was evaluated visually using plots and quantitatively using Root Mean Square Error (RMSE). Results indicate that applying PINN led to a significant RMSE reduction across all subjects, with improvements ranging from 67% to 89%, thereby highlighting the effectiveness of the proposed approach.

Hemodynamics is related to blood flows in the circulatory system under normal and pathological conditions to understand the mechanisms of various diseases and to treat them accordingly. Different methods, with their own advantage and weaknesses, have been adopted for hemodynamic studies. In this dissertation, two new strategies are developed by combining different methods, such as Magnetic Resonance Imaging (MRI), Computational Fluid Dynamics (CFD), and Physics-informed Neural Network (PINN) based on physical information and applied them for the quantitative study of hemodynamics. The strategies take full advantage of each method, allowing better quantification of hemodynamics and better prediction of the outcome of surgical protocols. Specifically, the first strategy, combining MRI and CFD, for personalized stent intervention in aortic coarctation was proposed. To validate the accuracy of CFD, I first performed numerical simulations using different turbulence modeling methods and compared the numerical results with experimental data from flow MRI. The validated CFD method is further used to study the blood flows within virtually deformed aortic geometries, and to guide stent implantation. Although only the aorta was considered, such a strategy can be extended to other stenosis, and can be used to help clinicians to evaluate surgical plans before intervention. The second strategy was proposed to accomplish blood flow prediction by combing MRI and PINN. Such a strategy overcomes the weaknesses of MRI and CFD for hemodynamics. Prediction of both laminar and turbulent blood flows with PINN in 3D-printed idealized and realistic aortic geometries was performed. Flow data and geometric information from the MRI were considered as inputs for the training. The obtained results show that image-based PINN can overcome the weaknesses of MRI and CFD, which are currently widely used for hemodynamic studies and can predict flow quantitatively using small amounts of noisy data. In summary, in this dissertation I have developed two new strategies by combining different methods for quantitative study of hemodynamics. Bringing together physics, medicine, and computer science, these strategies may shed light on precision medicine and personalized medical therapy.

On acoustic fields of complex scatters based on physics-informed neural networks